DOI: 10.1002/cphc.200900154 Spatiotemporal Kinetics in ...time.kaist.ac.kr/pub/49.pdf · Using...

$: DOI: 10.1002/cphc.200900154 Spatiotemporal Kinetics in ...time.kaist.ac.kr/pub/49.pdf · Using diffraction methods with modern sources and detection techniques, impressive progress$
DOI: 10.1002/cphc.200900154

Spatiotemporal Kinetics in Solution Studied by Time-Resolved X-Ray Liquidography (Solution Scattering)Tae Kyu Kim,[b] Jae Hyuk Lee,[a] Michael Wulff,[c] Qingyu Kong,[d] and Hyotcherl Ihee*[a]

1958 � 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim ChemPhysChem 2009, 10, 1958 – 1980

1. Introduction

Diffraction is the most common and accurate method for de-termining molecular structure on the atomic length scale.Using diffraction methods with modern sources and detectiontechniques, impressive progress has been made in unravelinghighly complex structures including biomolecules. For exam-ple, most three-dimensional structures of proteins have beendetermined by X-ray crystallography, where diffraction from awell-ordered protein single crystal is measured. Usually thestructures determined by diffraction methods represent theaveraged structure of the most stable configurations in equili-brium, but by adopting the pump–probe scheme commonlyused for time-resolved optical spectroscopy,[1–9] even transientstructures occurring in the course of a chemical reaction canbe obtained.[10–37] In this scheme, a reaction in the molecules isinitiated by an optical pulse (pump), and the time evolution ofthe induced structural changes is probed, at a given delay, bythe diffraction of a short X-ray or electron pulse that replacesthe optical probe pulse in time-resolved optical spectroscopy.

Time-resolved structural studies have been established byusing electron[10–24] and X-ray diffraction techniques.[25–35] Sinceelectrons and X-rays interact with matter quite differently,these two methods are highly complementary. Due to thenearly million-fold higher scattering cross section for electronsthan for X-rays, time-resolved electron diffraction has been ap-plied to the transient structural studies of dilute or thin sam-ples, such as molecules in the gas phase,[11–13, 15, 16] surfa-ces,[10, 17, 18] nanostructures,[19–22] and thin films.[23, 24] In contrast,X-ray pulses are capable of revealing transient structures ofbulk samples, such as crystals and liquids with a thickness inthe 10–100 mm range. Femtosecond X-ray sources, such as alaser-driven plasma[38] and an accelerator-based source,[39, 40]

have been used to investigate the dynamics of acoustic pho-nons, heating, nonthermal behavior near the melting point,and phase transitions in simple crystalline samples with~100 fs temporal resolution. In such cases, the system understudy is quite simple which means that the structural dynamics

can be probed by monitoring one or a few Bragg spots withtime. To follow the atomic positions of all the atoms in morecomplex systems, almost all Bragg diffraction spots need to berecorded as a function of time, and thus the current femtosec-ond X-ray sources cannot be used due to their insufficientphoton flux. Instead, high-brilliance synchrotron sources havebeen used to study transient structural changes in small organ-ic,[41, 42] inorganic,[43, 44] and complex protein molecules[45–47] incrystals. For example, the conformation changes of proteinsduring their biological function have been tracked, in singlecrystals, by time-resolved Laue crystallography with 100 pstime resolution.[45–47]

All the samples mentioned so far are either single crystals orin polycrystalline form. During the last decade it has beendemonstrated that the transient structures can be capturedeven in liquid samples by using the same time-resolved diffrac-tion (scattering) method. To distinguish the applications forliquid samples from other studies on crystalline samples, wepropose to call it time-resolved X-ray liquidography (TRXL).[25–

35] TRXL is a technique that can be used to unravel intermedi-ate structures and their spatiotemporal kinetics in the solutionphase where most reactions relevant to chemical synthesis, bi-

[a] J. H. Lee, Prof. H. IheeCenter for Time-Resolved Diffraction, Department of ChemistryGraduate School of Nanoscience & Technology (WCU), KAISTDaejeon 305-701 (Republic of Korea)Fax: (+ 82) 42-350-2810E-mail : [email protected]

[b] Prof. T. K. KimDepartment of Chemistry and Institute of Functional MaterialsPusan National University, Busan 609-735 (Republic of Korea)

[c] Prof. M. WulffEuropean Synchrotron Radiation Facility6 Rue Jules Horowitz, BP 220, 38043 Grenoble Cedex (France)

[d] Dr. Q. KongSoci�t� Civile Synchrotron SOLEIL, L’Orme des MerisiersSaint-Aubin BP 48, 91192 Gif-sur-Yvette Cedex (France)

Information about temporally varying molecular structureduring chemical processes is crucial for understanding themechanism and function of a chemical reaction. Using ultra-short optical pulses to trigger a reaction in solution and usingtime-resolved X-ray diffraction (scattering) to interrogate thestructural changes in the molecules, time-resolved X-ray liquid-ography (TRXL) is a direct tool for probing structural dynamicsfor chemical reactions in solution. TRXL can provide directstructural information that is difficult to extract from ultrafastoptical spectroscopy, such as the time dependence of bondlengths and angles of all molecular species including short-lived intermediates over a wide range of times, from picosec-onds to milliseconds. TRXL elegantly complements ultrafastoptical spectroscopy because the diffraction signals are sensi-tive to all chemical species simultaneously and the diffractionsignal from each chemical species can be quantitatively calcu-

lated from its three-dimensional atomic coordinates and com-pared with experimental TRXL data. Since X-rays scatter fromall the atoms in the solution sample, solutes as well as the sol-vent, the analysis of TRXL data can provide the temporal be-havior of the solvent as well as the structural progression of allthe solute molecules in all the reaction pathways, thus provid-ing a global picture of the reactions and accurate branchingratios between multiple reaction pathways. The arrangementof the solvent around the solute molecule can also be extract-ed. This review summarizes recent developments in TRXL, in-cluding technical innovations in synchrotron beamlines andtheoretical analysis of TRXL data, as well as several examplesfrom simple molecules to an organometallic complex, nanopar-ticles, and proteins in solution. Future potential applications ofTRXL in femtosecond studies and biologically relevant mole-cules are also briefly mentioned.

ChemPhysChem 2009, 10, 1958 – 1980 � 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.chemphyschem.org 1959

www.chemphyschem.org

ology, and industrial applications occur. For studying the struc-tural dynamics of molecules in solution, time-resolved X-rayabsorption spectroscopy[48–50] serves as a complementary tool.A brief comparison of TRXL and time-resolved X-ray absorptionspectroscopy will be given below along with a comparison ofTRXL and time-resolved optical spectroscopy.

In the solution phase, the solute species (molecules, ions, oratoms of interest) are dissolved in a solvent that in most cases

outnumbers the solute. Since X-rays scatter and diffract fromall atom–atom pairs, the signal has three principal contribu-tions: i) the solute-only term from the internal structure of thesolute molecules, ii) the solvent-only term from the bulk sol-vent, and iii) the solute–solvent cross term from solute–solventatomic pairs. In general, the solvent-only term dominates theothers. For this reason, diffraction is not the most sensitivetool to elucidate the structure of a solute. In addition, the in-formation about the structural changes is contained in the dif-ference in the diffraction intensity measured with and withoutexcitation. Typically only a fraction of the solute species is ex-cited by the optical excitation. Therefore, the laser-inducedchange in the diffraction signal (difference diffraction intensity)is embedded in a strong background signal from the solvent.Upon photoexcitation, the solutes absorb photons and mightundergo various reaction pathways, which affects the solute-only and the solute–solvent cross terms. The absorbed photonenergy is eventually transferred to the solvent, thereby chang-ing the thermodynamic state of the solvent, that is, its temper-ature, pressure, and density. Therefore, the solvent-only termalso changes with time.[25, 26] In summary, the TRXL signal is ex-tremely weak with a low signal-to-noise ratio, but at the sametime it contains rich information about the structural changesof not only the solute but also the solvent. The analysis of

Tae Kyu Kim, born in 1976 in South

Korea, received his B.S. and M.S. de-

grees in chemistry at KAIST and his

PhD in physical chemistry at KAIST in

2004, investigating photodissociation

dynamics of small molecules and clus-

ters. Afterwards he worked with Prof.

Hyotcherl Ihee as a postdoctoral

fellow in KAIST and focused on the

structural dynamics of small molecules

in solution using time-resolved X-ray

liquidography. He is currently an assis-

tant professor at Pusan National University (Korea). He has lately, in

collaboration with Bob Schoenlein at the ALS, used ultrafast X-ray

absorption spectroscopy on photochemically interesting molecules

in solution.

Jae Hyuk Lee was born in 1983 in

South Korea, and received his B.S.

degree in chemistry at KAIST, South

Korea. He is a PhD candidate under

the supervision of Prof. Hyotcherl Ihee

at KAIST. He is investigating the struc-

tural dynamics of various molecular

systems ranging from small molecules

to proteins in the solution phase using

ultrafast X-ray liquidography.

Michael Wulff received a Masters

Degree in mathematics and physics

from the Niels Bohr Institute, Universi-

ty of Copenhagen, in 1981 and a PhD

in solid-state physics from the Cavend-

ish Laboratory, University of Cam-

bridge, in 1985. He then joined Gerry

Lander at the Transuranium Institute in

Karlsruhe (1985–1989) where he

worked on the magnetic structure of

actinides using neutron scattering. He

joined the European Synchrotron Radi-

ation Facility (ESRF) in 1990 as responsible for the Laue beamline

ID09. He received the M. T. Meyer Award from the University of

Cambridge in 1984. In 2001 he received the Rçntgen Medal from

the University of Wurzburg. In 2003 he was appointed Adjoin Pro-

fessor at the Niels Bohr Institute and in the Chemistry Department

at the University of Copenhagen.

Qingyu Kong, born in 1972 in China,

received B.S. and M.S. degrees in opti-

cal and laser physics at Shandong Uni-

versity in 1998 and a PhD in physical

chemistry at Fudan University, Shang-

hai, in 2001, on the formation and

photofragmentation reactions of met-

allofullerenes. Starting as a postdoc-

toral fellow as a beamline scientist

from 2003 to 2007, he worked with

Michael Wulff in ESRF, and focused on

time-resolved X-ray scattering on

small molecules in solution. From 2007 to the present, he is beam-

line scientist at the Soleil Synchrotron near Paris, studying catalytic

chemistry and lithium-ion batteries with time-resolved dispersive

EXAFS.

Hyotcherl Ihee obtained a B.S. from

KAIST and a PhD from Caltech in 2001

under the supervision of Prof. Ahmed

Zewail, developing ultrafast electron

diffraction. He then joined Prof. Keith

Moffat at the University of Chicago as

a postdoctoral fellow working on pro-

tein structural dynamics using time-re-

solved X-ray crystallography. In 2003,

he became a faculty member at KAIST

where he continues to contribute to

the advancement of TRXL. His current

research interests focus on molecular structural dynamics probed

by time-resolved electron/X-ray diffraction and spectroscopy.

1960 www.chemphyschem.org � 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim ChemPhysChem 2009, 10, 1958 – 1980

H. Ihee et al.


TRXL data requires accurate theoretical modeling, which in-volves quantum calculations, molecular dynamics (MD) simula-tions, and global-fitting analysis. We have recently revealed thestructural reaction dynamics of several interesting molecules insolution by TRXL, with innovations in synchrotron and beam-line technology and developments in data analysis.[25–35]

This review focuses on the experimental technique, the dataanalysis, and examples of how TRXL reveals structural dynam-ics and kinetics in solution. The enormous advances in time-re-solved X-ray diffraction from crystalline materials and surfa-ces[38] and in time-resolved X-ray absorption spectroscopy incondensed systems[48–50] are not the subjects of this article. Thereview is organized as follows. In Section 2, the basic experi-mental and theoretical concepts of TRXL are discussed. This isfollowed by a review of recent TRXL studies with emphasis onphotochemistry in the solution phase (Section 3). The applica-tion examples include simple molecules, organometallic com-plexes, nanoparticles, and protein molecules in solution. Finally,the perspectives of extending TRXL to femtosecond studiesand biologically relevant molecules are briefly presented.

2. Experiment and Analysis of TRXL

2.1. Basic Principle of Liquid X-ray Diffraction and Scatter-ing

The general theory of X-ray diffraction from a disorderedsample is well established.[51–53] This section summarizes thebasic formulas used in structure determination from TRXL data.X-ray diffraction from a disordered sample is often called dif-fuse scattering to distinguish it from the diffraction from well-ordered crystalline planes (Bragg diffraction). The system underconsideration is a spatially isotropic liquid. When scatteringand diffraction from an optically excited system is considered,the system might not be isotropic just after the excitation dueto the possible polarization of the exciting light.

However, since the X-ray pulse length in our synchrotron dif-fraction studies is rather long (~100 ps) compared with the ro-tation time of small molecules in solution (~10 ps), we can ap-proximate the system to be isotropic. In addition, the ratherlong X-ray pulse length allows us to treat the system as beingin quasi-equilibrium during the exposure, although the struc-tures might change over longer times. The X-ray diffraction in-tensity is typically expressed as a function of q, the momen-tum transfer between the incident (k0) and the elastically scat-tered (k) X-ray waves (see Figure 1). The magnitude of q is a

function of the X-ray wavelength and the scattering angle 2 q

between k and k0 as shown in Equation (1):

q ¼ 4p

lsin q ð1Þ

The basic expression for the amplitude of the diffracted elec-tric field, neglecting multiple scattering, is given by Equa-tion (2):

AðqÞ ¼Z

1eðrÞ expð�iq � rÞdr ð2Þ

where 1e(r) is the electron density of the sample. Since we areinterested in the atomic positions rn, we express the total elec-tron density in the sample as a superposition of electron densi-ties centered on the atomic positions [Eq. (3)]:

1eðrÞ ¼X

n

1n r� rnð Þ ð3Þ

where 1n is the electron density of the nth atom and r is a cer-tain position from the origin. The combination of Equations (2)and (3) leads to the new expression [Eq. (4)]:

AðqÞ¼Z X

n

1e r� rnð Þ expð�iq � rÞdr

¼X

n

expð�iq � rnÞZ

1n r� rnð Þ exp �iq � r� rnð Þð Þd r� rnð Þ

¼X

n

fnðqÞ exp �iq � rnð Þ

ð4Þ

with a new function, fn(q), for the scattering from the nth atom(the so-called atomic form factor), which is the Fourier trans-form of the electron density of atom n [Eq. (5)]:

fnðqÞ ¼Z

1nðrÞ exp �iq � rð Þdr ð5Þ

Since the atom can be approximated as a spherical object,fn(q) depends only on the modulus of q, that is, fn(q). Usuallythe atomic form factor for a specific atom can be approximat-ed by the following expression [Eq. (6)]:

f ðqÞ ¼X4

i¼1

ai exp �bi q=4pð Þ2ð Þ þ c ð6Þ

where the parameters ai, bi, and c are tabulated Cromer–Mannparameters.[54] In fact Equation (6) is an angularly averagedform of Equation (5). Since the scattering intensity is thesquare modulus of the scattering amplitude, the scattered in-tensity, Selastic(q) of elastic scattering can be described by Equa-tion (7):

Figure 1. Schematic representation of the scattering geometry: the relation-ship between the incoming X-ray (k0), the scattered X-ray (k), and momen-tum transfer vector q.


Spatiotemporal Kinetics in Solution


SelasticðqÞ¼X

n

fnðqÞ exp �iq � rnð Þ��

��2

¼X

n

Xm

fnðqÞfmðqÞ exp �iq � rn � rmð Þð Þð7Þ

where indexes m and n include all atoms in the sample. Innoncrystalline materials such as liquids and gases, the mole-cules are randomly oriented. The symbol S is used for scatter-ing intensity and should not be confused with entropy. Theisotropic averaging of Equation (7) leads to the Debye Equa-tion [Eq. (8)]:

SelasticðqÞ¼X

n

Xm

fnðqÞfmðqÞ exp �iq � rn � rmð Þð Þ* +

W

¼X

n

Xm

fnðqÞfmðqÞ 1=4pð ÞZp

0

exp �iqrnm cos að Þ2p sin a da

¼X

n

Xm

fnðqÞfmðqÞsin qrnm

qrnm

¼X

n

f 2n ðqÞ þ

Xn

Xm6¼n

fnðqÞfmðqÞsin qrnm

qrnm

ð8Þ

Here, rnm is the distance between the nth and mth atoms. In re-ality, this expression is not convenient to use for the liquidphase because of the large number of possible combinationsof n and m. Instead, if 1ij(r) is defined as the density of the i-type atom around the j-type atom at a distance r, there are4pr21ij(r)dr of the j-type atoms in the distance range r to r + drfrom an i-type atom, and Equation (8) becomes [Eq. (9)]:

SðqÞ ¼X

i

Nif2

i ðqÞ þX

i

Xi 6¼j

NifiðqÞfjðqÞZ

v4pr21ijðrÞ

sin qrqr

dr

ð9Þ

where the indexes i and j now run over the different atomtypes and Ni is the number of i-type atoms. This is a more gen-eral expression of the scattered intensity for an amorphoussample. As the distance r increases, the density 1ij convergesto the average density (10j) of the j-type atom in the sample.The scattered intensity from this average atom density is com-pletely negligible except at small scattering angles, often notaccessible in the experiment because it is too close to the pri-mary (non scattered) X-ray beam. Accordingly the scatteringintensity at small angles can be subtracted from Equation (9)on the basis that it is negligible in the range of observableangles. In this case, the scattering intensity of the third term ofEquation (10 a) is negligible and can be expressed by Equa-tion (10 b):

SðqÞ ¼X

i

Nif2

i ðqÞ þX

i

Xi 6¼j

NifiðqÞfjðqÞZ

v4pr2 1ijðrÞ � 10j

� � sin qrqr

dr

þX

i

Xi 6¼j

NifiðqÞfjðqÞZ

v4p210j

sin qrqr

dr

ð10aÞ

SðqÞ ¼X

i

Nif2

i ðqÞ þX

i

Xi 6¼j

NiNjfiðqÞfjðqÞZ

v4pr210 gijðrÞ � 1

� � sin qrqr

dr

ð10bÞ

where gij(r) is the pair distribution function between atomtypes i and j. The radial distribution function (RDF) is definedsuch that 4pr2gij(r)dr is the probability of finding a j-type atomat the distance r from an i-type atom. Equations (8) and (10)are important in the theoretical modeling of experimentalTRXL data. The difference diffraction signal in TRXL measure-ments has three contributions as explained in Section 1. Like-wise one can separate the RDF [gij(r) in Eq. (10)] into three dif-ferent contributions as shown in Figure 2. The first contribu-

tion is the gij(r) of the solute. In this case i and j represent theatoms within the molecule and gij(r) describes its (internal)structure. The gij(r) functions are usually very sharp at intera-tomic distances (typically 2–5 � for small molecules, but canbe longer for larger molecules). Correlations between differentsolutes are usually negligible in diluted solutions. For example,for CHI3 dissolved in CH3OH[32] at a concentration of 20 mm,the average distance between CHI3 molecules is ~27 �. Thesecond contribution is the gij(r) of the solvent. This term de-scribes the structure of bulk solvent and thus is dependent onthe thermodynamic variables, that is, temperature, pressure,and density. The third contribution is the gij(r) for the solute–solvent cross term. This represents the structure of the solventaround the solutes. An example of gij(r) and the correspondingscattering intensity S(q) is shown in Figure 3 for I2 dissolved inCCl4.

The structural dynamics information is contained in thechange in the scattered intensity as a function of time, DS ACHTUNGTRENNUNG(q,t).

Figure 2. Schematic representation of the three principal gij(r) contributionsfor the C2H4I2 molecule dissolved in methanol. The C, H, and I atoms are col-ored in green, blue, and purple, respectively. The solvent is shown in gray.Red arrows indicate interatomic pairs for the solute only and the blue andgreen arrows represent solute–solvent and solvent-only pairs, respectively.


H. Ihee et al.


Since the scattered signal is proportional to Z2 (Z = atomicnumber), solute molecules with heavy atoms increase the rela-tive ratio of the solute-related terms, DSsolute only ACHTUNGTRENNUNG(q,t) and DSsolute–

solventACHTUNGTRENNUNG(q,t), against the solvent-only term DSsolvent onlyACHTUNGTRENNUNG(q,t). Figur-e 4 a compares the solvent-only and solute-only terms for thephotodissociation of Cl2 and I2 in CCl4. The solute-only term iscomparable to the solvent-only term for I2 in CCl4, but it ismuch smaller for Cl2 in CCl4.

Although the scattered intensity probes all structures in thesolution mixture, a more intuitive real-space interpretation isobtained by sine-Fourier transforming qS(q) into a radial densi-ty S(r) [Eq. (11 a,b)]:

SðrÞ ¼ 12p2r

Z 1

0qSðqÞ sinðqrÞdq ¼ C

V

Xi 6¼j

wij gijðrÞ � 1� �( )

ð11aÞ

wijðrÞ ¼Z 1

0dqfiðqÞfjðqÞ cosðqrÞ ð11bÞ

where C is a constant, the wij are weighting coefficients, and Vis the volume of the system. By defining S(r) in this way onecan obtain information on the average gij(r) weighted by theX-ray form factors.

So far we have described the elastic scattering, which con-tains the average molecular structure of the solution. However,X-ray photons also scatter inelastically with the scattered X-rays having slightly longer wavelengths. Since inelastically scat-tered waves do not interfere, the inelastic scattering is inde-pendent of structure; it depends only on the number and type

of atoms in a molecule. The inelastic scattering intensity canbe calculated with Equations (12) and (13):

SinelasticðqÞ ¼ Z � SelasticðqÞZ

� �

� 1�M exp �Kq=4pð Þ � exp �Lq=4pð Þ½ �f gð12Þ

SinelasticðqÞ ¼ Za

1þ bq=4pð Þc

� �ð13Þ

where Z in Equation (12)[55] is the atomic number, and K, L, andM are atomic constants. Equation (13)[56] is for heavier atoms,from Ca to Am. The inelastic intensity increases with q (Fig-ure 4 b). The inelastic intensity does not change during the re-action because it does not depend on structure and the factthat the mass of the involved atoms is conserved. It is usefulto include the inelastic scattering term for finding the absolutescattering from the sample. For the sake of comparison, theelastic and inelastic intensities for I2 in the gas phase areshown in Figure 4 b. The magnitude of the inelastic intensity ismuch smaller than that of the elastic scattering intensity atlower q, but as q increases, the inelastic scattering intensity in-creases while the elastic scattering intensity decreases.

Figure 3. gij(r) for the atom–atom pairs for I2 in CCl4. a) gij(r) for I2 (solute-onlyterm); b) gij(r) for the solvent pairs C–C, C–Cl, and Cl–Cl in CCl4 (solvent-onlyterm); and c) gij(r) for the solute–solvent cross term. The gij(r) values are cal-culated in equilibrium by MD simulation for one I2 molecule in 256 CCl4 mol-ecules. d) Scattering intensity for each contribution calculated with the gij(r)values by using Equation (10). The solvent scattering (blue line) is the sumof S(q) curves from C–C and Cl–Cl pairs, and the solute–solvent cross term(dark cyan) is the sum of the S(q) curves for the I–C and I–Cl pairs. Thesolute-only scattering intensity (red) is calculated from the gij(r) of I–I. The in-tensities of the solute–solvent cross term and the solute-only term are multi-plied by 10 to enhance their visibility. Because the ratio of solute to solventmolecules is extremely small, the scattering intensity from the solvent domi-nates the total scattering.

Figure 4. a) Comparison of DSsolvent only(q) and DSsolute only(q) curves for the pho-tolysis of Cl2 and I2 in CCl4. Typical DSsolvent only(q) curves at 100 ps and 1 msare shown in black and blue broken lines, respectively. DSsolute only(q) curvesfor the photolysis of Cl2 and I2 in CCl4 are shown as red and green solidlines, respectively. b) Intensities for I2 in the gas phase. The black curve is thesum of elastic and inelastic scattering. The blue curve is the inelastic scatter-ing multiplied by 10. The green curve is 2 f2(q) for an iodine atom, the first(self) term in Equation (8), and the red curve is the second (interference)term in Equation (8).




2.2. TRXL Experiments

In a time-resolved X-ray experiment, we need to initiate agiven reaction and then open the X-ray shutter and record theX-ray scattering as a function of time. Unfortunately the timeresolution of large-area charge-coupled device (CCD) detectors,which are essential for capturing a large fraction of the scat-tered beam, is milliseconds at best. This time resolution is sig-nificantly longer than the ultrafast timescales in chemical reac-tions. The pump–probe method is therefore used to improvethe time resolution at the cost of lowering the data collectionefficiency. The sample is excited by a short laser pulse and thestructure of the sample is probed by a delayed X-ray pulse, asin time-resolved laser spectroscopy. With the advent of third-generation synchrotrons, pulsed hard X-ray pulses with a pulselength of ~100 ps are now available and can be used for time-resolved experiments. However, the time separation of X-raypulses from a synchrotron ranges from a few nanoseconds tohundreds of nanoseconds, which is significantly shorter thanthe readout time of a conventional area detector. To reach theultimate time resolution limited by the X-ray pulse lengthitself, it is necessary to isolate a single pulse from the adjacentpulses with a mechanical chopper. Since the chopper greatlydecreases the flux of the X-ray photons (ph s�1), the polychro-matic beam from a narrow-bandwidth undulator is often usedin solution experiments where the q resolution can be relaxedto increase the signal-to-noise ratio. These approaches havebeen implemented on beamline ID09B at the European Syn-chrotron Radiation Facility (ESRF) and the subsection below de-scribes this in more detail. Figure 5 a shows the TRXL scheme.It comprises a closed capillary jet (or an open-liquid jet) thatsupplies a fresh sample for every laser/X-ray pulse pair, a short-pulse laser, a high-speed chopper that selects single X-raypulses, and an integrating area detector.

2.2.1. Laser-Excitation and X-ray-Probe Scheme

In a typical TRXL experiment, an ultrashort (100 fs–2 ps) opticallaser pulse initiates a photochemical process in a molecule ofinterest in the solution phase, and a 100 ps X-ray pulse from asynchrotron is sent to the volume to probe the structural dy-namics. The X-ray diffraction patterns are measured as a func-tion of the time delay between the excitation laser pulse(pump) and the X-ray pulse (probe). The time resolution is de-termined by several factors, such as the temporal durations ofpump and probe pulses and the timing jitter between twopulses.

2.2.2. Pulsed X-rays from the Synchrotron

Most TRXL measurements have been performed on beamlineID09B at the ESRF, which is dedicated to a variety of pump–probe experiments.[26, 28–33, 35] The ESRF, which was inauguratedin 1994, is a third-generation synchrotron and is specifically de-signed to produce very intense, collimated beams of hard X-rays between 5 and 100 keV (0.1–2.5 �). The electrons in thestorage ring are accelerated to 6.03 GeV in the 844-m-long

storage ring. Synchrotron sources typically deliver 50–150 ps X-ray pulses of polychromatic radiation. At ESRF, the electronbunches rotate around the storage ring in 2.82 ms, which corre-sponds to an X-ray frequency of 355.4 kHz. In uniform fillingmode, the electrons are evenly spaced and separated by2.84 ns. This filling mode is not suitable for TRXL because it isimpossible to select single pulses with a mechanical chopperfrom such a densely filled pulse train. The solution is to use fill-ing patterns with fewer bunches, such as the one-bunch, four-bunch, 16-bunch, or hybrid mode. The 16-bunch mode is wellsuited for TRXL liquid experiments in which 16 electron bunch-es (90 mA) are evenly spaced by 176 ns. The bunch length isabout 100 ps (full width at half maximum, FWHM) and a singlepulse can be isolated by the high-speed chopper on beamlineID09B.

Figure 5. a) Experimental setup for a TRXL experiment. X-rays from a syn-chrotron are guided through a beamline and selected by a high-speed me-chanical X-ray chopper. The chopper consists of a flat triangular disk spin-ning at the same frequency as the laser. The laser pulses excite the sampleand the time-delayed X-ray pulses probe the photoinduced structuralchanges as diffraction images on the CCD detector. The difference diffractionimage for a given positive time delay is generated by subtracting the refer-ence image at �3 ns from the diffraction image. b) Spectral shape of an X-ray pulse generated by the U17 undulator. To increase the signal-to-noiseratio the raw quasi-monochromatic (3 % bandwidth) X-ray beam is used.c) Picture of the TRXL setup on ID09B. The blue and orange lines representthe paths of the X-ray and laser beams, respectively. Both beams are over-lapped in the most stable region of the jet (300 mm thickness). Diffractionpatterns from the scattered X-rays are recorded by a MarCCD detector.


H. Ihee et al.


The X-ray pulses are generated by a 236-pole in-vacuum un-dulator with a magnetic period of 17 mm (U17) with magnetsinside the vacuum vessel of the storage ring. The undulatorspectrum can be shifted in energy by varying the distance be-tween the undulator magnets, the undulator gap, from 15 keVat the closed gap position at 6 mm to 20.3 keV at the opengap position at 30 mm. At a 9 mm gap, the undulator spec-trum is dominated by its first harmonics, which peaks at~18.0 keV (l= 0.67 �) with a ~3 % bandwidth. This quasi-mon-ochromatic beam is used to increase the flux and hence short-ens the exposure time by a factor of 250 over strictly mono-chromatic experiments with silicon crystals (Figure 6 b). The X-ray beam is focused by a platinum-coated toroidal mirror intoa spot size of 0.1 � 0.06 mm2. Each X-ray pulse delivers ~109 X-ray photons to the sample and its duration varies from 90 to150 ps depending on the bunch charge in the fill pattern. Thefrequency of the X-ray pulses from a 16-bunch fill is 5.7 MHz,that is, much faster than a normal amplified femtosecond laserthat typically operates around 1 kHz. Since laser and X-raypulses have to arrive on the sample in pairs, the frequency ofthe X-ray has to be lowered to that of the laser, which is ac-complished by a high-speed chopper (Julich). The mechanicalchopper is a flat triangular disk that is spinning at the frequen-cy of the laser. One of edges of the triangular rotor has a shal-low channel that terminates with small roofs. The channel isthus a semi-open tunnel with slits at the ends. When the

tunnel is parallel to the direction of the beam, the single X-raypulse is selected. The short (225 ns) opening window and thelow rotation jitter (3–4 ns) ensure the selection of single pulsesfrom the 16-bunch mode (176 ns pulse separation) at 1 kHz.

2.2.3. Laser System

High-intensity laser pulses are needed to excite a significantfraction of the sample. The laser pulse length has to be shorterthan or similar to the X-ray pulse length to keep the time reso-lution as high as possible. For most experiments, we use a Ti-sapphire-amplified femtosecond laser system producing~100 fs pulses at 780 nm with a pulse energy of ~2.5 mJ at arepetition rate of 986.3 Hz in phase with the mechanical chop-per. By frequency doubling and tripling in a beta bariumborate (BBO) crystal, we typically obtain 800 and 250 mJ pulse�1

at 390 and 260 nm, respectively. Typically the laser pulse istemporally stretched to 2 ps by passing it through fused-silicaprisms to prevent multiphoton excitation in the sample. Thelaser beam is focused to a spot size of 0.12 � 0.12 mm2 with a108 angle with the X-ray beam. Great care is taken to removeinhomogeneities in the beam profile through the use of spatialfilters.

A pump–probe experiment relies on the reproducibility ofthe time delay between pump and probe pulses. Therefore,the laser pulse has to be accurately synchronized to the X-raypulse. As described in the previous section, the mechanicalchopper isolates a subtrain of pulses at 986.3 Hz, the 360thsubharmonic of the radio-frequency (RF) clock. A phase shiftergenerates the delayed RF clock, which is synchronized with therepetition rates of the laser oscillator (88.05 MHz) and the am-plifier (986.3 Hz). The amplified laser pulse is in phase with thechopper. The time delay between the laser and X-ray pulses iscontrolled electronically by shifting the phase of the oscillatorfeedback loop with a delay generator with 10 ps resolution.Longer delays (>10 ns) are realized by amplifying a differentseed pulse of the oscillator pulse train. In this way the timedelay between the laser and X-ray pulses can be varied bychanging the arrival time of the laser pulse. The jitter betweenthe laser and X-ray pulses is less than 5 ps (rms) as measuredby a fast GaAs detector (see the following section).

2.2.4. Spatial and Temporal Overlaps

To increase the signal-to-noise ratio of the TRXL data and todefine the accurate time delay, the laser and X-ray pulses haveto be overlapped at the sample, in space and time. To checkthe temporal overlap, a fast GaAs detector is placed at thesample position and the laser and X-ray pulses are recorded inone time trace. With a 6 GHz oscilloscope, the relative timingcan be adjusted within a few picoseconds by moving the laserfiring time. During an experiment, the relative timing betweenthe laser and X-ray pulses is monitored simultaneously andnonintrusively by using fast photodiodes.

The spatial overlap between X-ray and laser pulses is ob-tained by replacing the sample with a 25-mm-diameter laserpinhole. This allows for checking the laser–X-ray overlap and

Figure 6. Raw diffraction patterns and curves for CHI3 in methanol recordedby the MarCCD detector. a) Left : raw diffraction image at �3 ns used as areference for the unperturbed sample; middle: raw diffraction image at 1 ms;right: difference diffraction image at 1 ms after radial integration. Theshadow in the upper part of each image is from the nozzle, and can be elim-inated by using a better nozzle. b) Radial integrated diffraction intensitycurves [S(q)] at 1 ms (black, barely visible) and �3 ns (red). The two curvesnearly coincide with each other. The difference intensity [DS(q)] at 1 ms timedelay (blue) is obtained by subtracting the normalized S(q) at �3 ns fromthe normalized S(q) at 1 ms. The total intensity curves are normalized to 1 inthe range 458�2 q�558, which forces the curves to cross zero in this range.DS(q) is typically 1000 times weaker than S(q). The DS(q) curve is multipliedby 100 for clarity.




for scanning the laser-beam profile. The pinhole is centered onthe X-ray beam and then the laser spot is moved across thecenter of the pinhole by scanning the position of the focusinglens. For centering the spatial overlap more precisely, thechange in the scattering caused by thermal expansion is used,which in a liquid and with the present beam sizes appearsafter 1 ms. Specifically, we scan the ratio of the scattered inten-sity between the inner and outer disks of the solvent peak.When the sample has expanded after typically 1 ms, the liquidpeak will shift to lower scattering angles. The low-angle scat-tering increases and the high-angle scattering decreases.Therefore, the ratio between the inner and outer parts of thesolvent peak changes in proportion to the laser excitation. TheX-ray beam is typically 60 mm vertically and 100 mm horizontal-ly. The laser spot is circular in shape with a diameter of 100–200 mm.

2.2.5. Data Acquisition

The scattered X-ray signals are recorded on a 133-mm-diame-ter MarCCD detector (recently upgraded to the ESRF/FrelonCCD camera; here we report the MarCCD parameters), which isplaced ~45 mm downstream of the sample. This allows scatter-ing angles (2 q) from 3 to 608 to be covered. The scattered X-rays are converted into visible light on a phosphor screen inthe camera and the image is transferred onto the CCD chipsvia a fiber-optic taper with a demagnification of 2.7. Scatteringimages are recorded on a square CCD (2048 � 2048 pixels) withan effective pixel size of 64.276 mm. The quantum efficiency at18.0 keV is ~50 % and the gain in the conversion of X-ray toCCD counts is 1 arbitrary digital unit (ADU) per 18.0 keV X-rayphoton. The CCD chip is cooled to �70 8C to reduce the darkcurrent to about 0.02 ADU s�1. The readout noise is 0.1 ADUpixel�1. The typical exposure time is less than 5 s, and typically5 � 109 X-ray photons per image are recorded by the CCD de-tector. The data acquisition protocol is worked out to minimizethe effect of slow drifts in the beam positions, in the detectorand in the sample (heating, radiation damage). Diffraction dataare typically collected for more than ten time delays spanningfrom �100 ps to 3 ms, and each time delay is interleaved by ameasurement at �3 ns which serves as a reference for the un-perturbed sample. Each time sequence is typically repeatedmore than ten times to make it easier to discriminate badmeasurements.

2.2.6. Sample System

Two different sample-cell systems have been used: a dilute sol-ution (0.5–100 mm) or a pure solvent is circulated througheither a capillary or an open-jet sapphire nozzle to provide astable sheet of flowing liquid with a thickness of ~0.3 mm.Likewise the diameter in the capillary system is 0.3 mm. In theopen-jet nozzle the solution is passed between two flat sap-phire crystals with a spacing of 0.3 mm (Kyburz), which makesa stable liquid sheet that is directly exposed to the laser/X-raybeams. The open-jet system has the advantage that the scat-tering from the capillary is eliminated, which reduces the back-

ground substantially, especially in low-Z liquids such as water.In addition, the capillary is often pierced by the laser beam orthe flow is reduced due to deposits inside the capillary. Theliquid jet is circulated with a speed of ~3 m s�1, fast enough toseparate the laser-heated portions of the flowing solution inthe 986.3 Hz laser pulse train. The solution from the jet is col-lected and recycled by passing it through a reservoir.

2.3. Analysis of TRXL Data

2.3.1. Data Reduction—Difference Diffraction Curves

In this section, we describe the data-reduction routines usedto generate difference diffraction curves at a specific timedelay. The two-dimensional diffraction patterns on the CCD arecircularly integrated into one-dimensional diffraction curves [S-ACHTUNGTRENNUNG(q,t)] as a function of the momentum transfer q and the timedelay t. During this process the effect of the X-ray beam polari-zation and the effective phosphor-screen thickness (as a func-tion of the scattering angle) is removed. The major difficulty inthe data reduction is that the total diffraction intensity con-tains contributions not only from the solute but also from thesolvent, air, and so on.

Figure 6 shows that time-resolved differences are small andtherefore care has to be taken before subtraction. In particular,small (0.01 %) variations of the scattered intensity can maskthe effect of the laser excitation. Since the best I0 detector forX-ray intensity on ID09B is reliable “only” to about 3 � 10�4, thistype of detector cannot be used for normalization purposes.Instead, the intensities of the total diffraction curves are nor-malized to 1 at high 2 q angles, in the range from 45 to 558,which makes the difference diffraction curve cross zero in thisrange. The assumption is that the signal from any structuralchange in the solute will oscillate several times around zero inthat wide interval, thus ensuring that the curve integral is zero.In addition, the diffraction curve is less sensitive to thechanges in solute structure in this 2 q range because the mag-nitude of the interference oscillation from interatomic distan-ces is greatly damped, that is, atomic scattering dominates inthis region. After normalization, the diffraction curve for theunperturbed sample is subtracted from the curve at a positivetime delay to generate the difference diffraction curve [DS-ACHTUNGTRENNUNG(q,t)] . Then the difference diffraction curve can be put on anabsolute scale, defined by the scattering from one solvent mol-ecule, by scaling it to the nonexcited solvent/solute back-ground (including both elastic and inelastic contributions). Toconvert the difference intensity in absolute electron units persolvent molecule, the raw scattering intensities are comparedwith the theoretical intensity from one solvent molecule simu-lated by MD. Once the scattering intensity from a MD simula-tion is scaled to one solvent molecule, experimental raw scat-tering intensities can be compared with the theoretical model.Experimental difference curves are further scaled down by nor-malization factors. In summary, we need to consider the ratiobetween experimental raw data and theoretical curves, as wellas the normalization factor. As shown in Figure 6, the changes


H. Ihee et al.


in diffraction intensity are generally much smaller (less than0.1 %) than the total diffraction signal.

To magnify the intensity at high angles (where the signalfrom the solute-only term dominates the total differencesignal), DS ACHTUNGTRENNUNG(q,t) is multiplied by q (Figure 7). The qDS ACHTUNGTRENNUNG(q,t) curves

amplify the high-resolution part, that is, changes in atom–atom correlations inside molecules, and that function enters di-rectly when calculating the Fourier transform. As expected, the�100 ps curve shows no difference intensity and the differencefeatures only start to appear at positive time delays. It is moreintuitive to consider the sine-Fourier transforms, rDS ACHTUNGTRENNUNG(r,t), ofqDS ACHTUNGTRENNUNG(q,t), where r is the interatomic distance. This real-spacerepresentation is a measure of the change in the radial elec-tron density for all atom–atom pairs. Positive and negativepeaks mean the formation and depletion of the specific intera-tomic distance, respectively. The relation between qDS ACHTUNGTRENNUNG(q,t) andrDS ACHTUNGTRENNUNG(r,t) is [Eq. (14)]:

rDSðr; tÞ ¼ 12p2

Z 1

0qDSðq; tÞ sinðqrÞe�q2adq ð14Þ

where a is a damping constant (typically a = 0.03 �2) for thereduction of truncation error caused by the finite accessible qrange (0.5–8.5 ��1) in the TRXL experiment.

Experimental qDS ACHTUNGTRENNUNG(q,t) and rDS ACHTUNGTRENNUNG(r,t) curves from the photodis-sociation of 1,2-diiodotetrafluoroethane (C2F4I2) dissolved inmethanol[33] are shown in Figure 7. Because the high-Z I atomsin the solute scatter X-rays more strongly than the low-Zatoms (C, H, and O) in the solvent, the signal from the solutestands out in the rDS ACHTUNGTRENNUNG(r,t) representation. For example, the neg-ative peak at ~5.0 � corresponds to the initial I···I distance inthe parent molecule. However, structure determination in solu-tion from TRXL data requires quantitative analysis of three con-tributions that are mutually connected by energy conservationin the X-ray-illuminated volume. In the following sections, wedescribe the theoretical analysis with the global-fitting ap-proach.

2.3.2. Data Analysis—Getting Scattering Components

For the global-fitting analysis in which theoretical differencecurves are fitted against the experimental data at all timedelays rather than one time delay at a time, the scatteringcomponents for the solute-related terms and the solvent-onlyterm need to be estimated theoretically. In fact these compo-nents are usually time-independent, which reflects the factthat most molecular transitions are ultrafast whereas their pop-ulation dynamics are slower. To calculate the scattering intensi-ties Sk(q) for all putative species during a chemical reaction, weuse the relationship between the RDFs gij(r) and S(q) [Eq. (10)] .The gij(r) for all atomic pairs in the solute-only and solute–sol-vent cross terms can be calculated by MD simulations with pu-tative solute structures from quantum chemical calculations.More specifically, geometry optimization and energy minimiza-tion of the solutes, their candidate intermediates, and theirfinal photoproducts in a solvent environment are calculated bydensity functional theory (DFT) using the code Gaussian 03.[57]

To describe the solvent environment, the integral-equation-for-malism polarizable continuum model (IEFPCM)[58] is used.These quantum chemical calculations provide optimized geo-metries and minimized energies for all putative chemical spe-cies. Using optimized geometries, MD simulations for all theputative species are performed. We use the MD programMOLDY,[59] which gives the gij(r) functions of all atomic pairs.MD simulations are performed in the (constant) NVT ensemble.Typically the simulation includes one solute molecule and hun-dreds of solvent molecules (range from 256 to 2048 mole-cules), and the solute molecule is initially placed in the centerof a virtual solvent box. As mentioned above, the internalstructure of each molecule is fixed; however, the intermolecu-lar interaction is governed by Coulomb forces and Lennard–Jones potentials. Consequently, from the MD-simulated gij(r)for a given solute in the solution, the associated X-ray intensityis then derived from [Eq. (15)]:

SðqÞ ¼X

ij

fiðqÞfjðqÞ Nidij þNiNj

V

Z1

0

gijðrÞ � 1� � sinðqrÞ

qr4pr2dr

0@

1A

ð15Þ

where fi(q) is the atomic form factor of the i-type atom, Ni isthe number of i-type atoms, dij is the Kronecker delta, and V isthe volume of the box. This equation is basically the same asEquation (10).

Using Equation (15), one can now calculate the intensity forall putative solutes. The gij(r) from atomic pairs within thesolute, the solute-only term, gives the intensity from a gas ofindependent molecules, which is calculated by the Debye for-mula in Equation (8). The solute–solvent cross terms can becalculated by using the gij(r) for solute–solvent pairs. In thisway, one can calculate the scattering components from all pu-tative solutes including their cage structures in the solvent.

We also need to understand the hydrodynamics of solventsafter energy transfer from solutes to the solvent. Initially (<1 ns) the transferred energy heats the solvent and the temper-

Figure 7. TRXL signals from photodissociation of C2F4I2 in methanol at select-ed time delays (100 ps, 300 ps, 1 ns, and 10 ns). a) Difference intensityqDS(q). Error bars represent the experimental error associated with eachscattering angle. b) Difference RDF rDS(r), the sine-Fourier transform of thecurves in (a).




ature and pressure build up at constant volume and densi-ty.[26, 35] This process can be described by a solvent-specific dif-ferential, (@S ACHTUNGTRENNUNG(q,t)/@T)1, which is hereafter referred to as (@S/@T).The scattering changes due to this term are mainly ascribedto the broadening of atom–atom distances in the solvent,constrained to a constant volume, by adiabatic heating at earlytimes. Then, thermal expansion sets in and the solvent even-ACHTUNGTRENNUNGtually returns to ambient pressure in typically 100 ns at aslightly elevated volume and temperature. Assuming localthermal equilibrium in the solvent, the change in the solventscattering, at a given time delay t, can be factorized as[Eq. (16)]:

DSsolventðq; tÞ ¼ DTðtÞ @S@T

1

þD1ðtÞ @S@1

T

ð16Þ

The two differentials [(@S/@T)1, and (@S/@1)T] can be obtainedin two ways: through MD simulations and a solvent-heatingexperiment. In the first case, MD simulations are performed asa function of the thermodynamic variables 1 and T. In the sim-ulations for methanol, for example, two temperatures (T1 = 300and T2 = 328 K) and densities (11 = 785.9 and 12 = 759.8 kg m�3)are used. The densities are chosen such that the system is atthe same pressure at (T1, 11) and (T2, 12). Three MD simulationsare run under the different thermodynamic conditions (T1, 11),(T2, 11), and (T2, 12). Then by taking the difference between thescattering in (T1 11) from that in (T2 11) and dividing by the tem-perature difference (T2�T1), the temperature differential at con-stant density [(@S/@T)1] is obtained. In the same way, subtract-ing the scattering intensity of the system in (T2 12) from that in(T2 11) and dividing by the density change (11�12) provides thedensity differential at constant temperature [(@S/@1)T] . The sol-vent differentials can also be obtained in a separate experi-ment in which the pure solvent is vibrationally excited, withoutinducing any structural change, with near-infrared light.[26] Theexperimental solvent differentials usually produce better fits inthe global analysis since they probe the real solvent responsewith the pink X-ray spectrum that is also used in the solute ex-periment. It should be noted that all calculated scattering com-ponents need to be corrected for slight polychromaticity ofthe X-ray beam, that is, the asymmetric 3 % bandwidth.

2.3.3. Data Analysis—Global-Fitting Analysis

In this section, we explain the global-fitting analysis[14, 28] whichfits the experimental data [qDSexp ACHTUNGTRENNUNG(q,t)] at all time delays insteadof fitting the data at each time delay separately. In fact all qDS-ACHTUNGTRENNUNG(q,t) curves at all time delays are linked together through thereaction kinetics due to total energy conservation. Global-fit-ting parameters generally include the rate constants for all re-actions, the fraction of excited molecules, the branching ratiosamong excited molecules, and the size of the laser spot at thesample. In some cases, the geometrical parameters (bondlengths and angles) and the energies of all putative speciescan also be included in the fitting. The first step is to generatethe theoretical difference diffraction curves qDStheACHTUNGTRENNUNG(q,t). As ex-plained, qDSexp ACHTUNGTRENNUNG(q,t) has three components (solute-only, solute–

solvent cross, and solvent-only terms) and qDStheACHTUNGTRENNUNG(q,t) can beexpressed by [Eq. (17)]:

DStheðq; tÞ ¼ DSsolute onlyðq; tÞ þ DSsolute�solventðq; tÞ þ DSsolvent onlyðq; tÞ

¼ 1R

Xk

ckðtÞSkðqÞ � SgðqÞX

k

ckð0Þ" #

|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}solute�only termþsolute�solvent cross term

þ @S@T

1

DTðtÞ þ @S@1

T

D1ðtÞ|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

solvent�only term

ð17Þ

where R is the ratio of solvent to solute molecules, k repre-sents the chemical species (reactant, intermediates, and prod-ucts), ck(t) is the fraction of k species after the time delay t,Sk(q) is the scattering intensity of species k, (@S/@T)1 is the scat-tering change with respect to the temperature rise in the sol-vent at constant density (temperature differential), (@S/@1)T isthe scattering response with respect to a change in solventdensity at constant temperature (density differential), and DT(t)and D1(t) are the changes of the solvent temperature and den-sity at time delay t, respectively. Equation (17) assumes thatthe diffraction changes from solute transitions are mathemati-cally locked to the solvent response by energy conservation inthe X-ray-probed volume.

To be more explicit we will now discuss a very simple reac-tion [Eq. (18)]:

R! R* ! I! P ð18Þ

where R is the ground state, R* is the state populated justafter excitation, I is an intermediate, and P is the final product.Because the structure of the solute changes, this gives thechanges in the diffraction intensity in the solute-only term.Also, the transformed solutes adopt new cage structures. Final-ly, the energy absorbed by the solute is transferred to the sol-vent and this causes a change in temperature, pressure, anddensity as a function of time. The structural displacements be-tween the solvent molecules are very small (typically milli-�),but given their large number, the signal from the temperatureand density changes is often comparable to the solute-relatedterms. Consequently we can connect the solute-related termsand solvent-only term by using the energy conservation pro-vided that we can calculate the energies of all species duringthe reaction. The underlying ideas are shown in Figure 8.

Once the time-independent intensities (Sk(q), (@S/@T)1, and(@S/@1)T) are determined, each experimental curve can be usedto find the best theoretical curve by using ck(t), DT(t), andD1(t) as fitting parameters. This approach has too many pa-rameters and the fits are unstable. To reduce the number offree parameters we use a global approach, in which theoreticaldifference curves are fitted at all time delays rather than onetime delay at a time. This consists in writing a system of differ-ential equations for the population of species and the energyin solution. Solving rate equations yields the theoretical ck(t)and Q(t) (heat into the solvent). DT(t), and D1(t) are also ob-tained from Q(t) by solving the hydrodynamics equations.Using this approach, the parameters that control the kineticsare the fitting parameters. For the model reaction of R!R*!


H. Ihee et al.


I!P, one can set the following rate equations [Eq. (19)]:

d R*½ �dt¼ �k1 R*½ �

d I½ �dt¼ k1 R*½ � � k½I�

d P½ �dt¼ k2 I½ �

ð19Þ

where k1 and k2 are rate constants for the R*!I and I!P reac-tions, respectively. Numerical integration of the rate equationsgives an estimation of the fraction of each species [ck(t)] to thetotal concentration as a function of time. From the estimatedck(t) and the energies Ek (J molecule�1) from the DFT calcula-tions, the heat transfer Q(t) to the solvent is calculated as afunction of time by using Equation (20):

QðtÞ¼ Energyðt ¼ 0Þ � EnergyðtÞ

¼ NA

R

Xk

Eg þ hn� �

ckð0Þ �X

k

Ek ckðtÞ" #

þNA

Rffast 1� exp �t=kfastð Þ½ �

ð20Þ

where NA is Avogadro’s number, R is the ratio of the numberof solvent molecules per solute, Eg (J molecule�1) is the abso-lute energy of the parent (ground-state) molecule, hn is the ex-citation energy, and Ek (J molecule�1) is the energy of species k.The symbol ffast denotes the fraction of rapid relaxed species,and kfast (s�1) is the rate constant for vibrational cooling whichoccurs faster than the temporal resolution of TRXL (~100 ps).Q(t) can be used to calculate the change in temperature [DT(t)]and density [D1(t)] as a function of time through the followinghydrodynamics relations (Livak equation, Eq. (21)):[60]

DPðtÞ ¼ aP

cTCV

Zt

�1

@Q@tðt0Þ exp � us=að Þ t � T 0ð Þð Þ2ð Þdt0

DTðtÞ ¼QðtÞ � CV � CPð Þ cT

aPDPðtÞ

CP

D1ðtÞ ¼10 cTDPðtÞ � aPDTðtÞ½ �

ð21Þ

where CV (J mol�1 K) and CP (J mol�1 K) are the heat capacity atconstant volume and constant pressure, respectively, cT is theisothermal compression constant, aP is the isobaric dilatationconstant, 10 is the density of the solvent, a is the radius of thelaser spot, and is us is the speed of sound in the solvent. Usingthe estimated values of ck(t), DT(t), and D1(t), one has DStheACHTUNGTRENNUNG(q,t)at all time delays from Equation (17). A least-squares fittingusing the chi-squared value between DStheACHTUNGTRENNUNG(q,t) and DSexp ACHTUNGTRENNUNG(q,t) isthe final step in the global-fitting analysis. The definition of chisquared (c2) used is [Eq. (22)]:

c2¼X

t

c2t

¼X

t

Xq

DStheðq; tÞ � DSexpðq; tÞ� �

sq;t

2 ð22Þ

The global fitting optimizes the rate constants for all reac-tions, the fraction of excited molecules, the fraction of reactedmolecules among excited molecules, the size of the laser spot,and the fraction of the vibrational cooling process. After mini-mization of chi squared for all time delays, the global-fittingprocess provides, as a function of time, chemical populationchanges and the temperature and density changes of the sol-vent. The overall scheme for the reduction and analysis ofTRXL data is presented in Figure 9.

3. X-ray Fingerprinting of Intermediates

TRXL has been used to capture the molecular structures of in-termediates and their reaction kinetics for various photochemi-cal processes. In the following, we present several applicationexamples that illustrate the rich variety of observables fromTRXL. Four different types of molecular systems have been

Figure 8. a) Energy transfer from photon-absorbing molecules (R) to the sol-vent. The ground state of the reactant R is laser-excited to the short-livedstate R* that decays, via vibrational cooling, to R and/or through a reactivepathway to the intermediate (I) and product (P) at times t2 and t3, respec-tively. The energy difference between the two species transfers to the sur-rounding solvent molecules. b) Time-dependent solute dynamics and sol-vent hydrodynamics properties (temperature and density) are linked byenergy conservation. Once the energy is transferred from the solute to thesolvent, the temperature and density of the solvent change as a function oftime. The fraction of excited molecules that return directly to the groundstate in a few picoseconds is denoted by ffast.




studied, simple molecules,[28, 29, 31–35] organometallic com-plexes,[30] nanoparticles, and proteins, covering a variety ofstructural problems in photochemistry. We emphasize here thedetermination of structures of transient intermediates, theircage structures, and the reaction kinetics.

3.1. Spatiotemporal Kinetics of Photoreaction

The photodissociation dynamics of HgI2 in the gas and solutionphases has been widely studied by various time-resolved spec-troscopic techniques.[29] Zewail and co-workers studied two-body dissociation by using laser-induced fluorescence monitor-ing,[61] and both two- and three-body dissociation have beenmeasured by time-resolved mass spectrometry.[62] In the solu-tion phase, the solvation dynamics of HgI2 in ethanol has beeninvestigated by femtosecond absorption spectroscopy.[63–65]

The vibrational relaxation and rotational dynamics of HgI2 gen-erated after impulsive dissociation have been discussed. De-spite ample information about the dynamics on short time-scales, a comprehensive mechanism spanning from picosec-onds to microseconds has been lacking. We applied TRXL toHgI2 and demonstrated that TRXL provides this information di-rectly. Figure 10 a shows the experimental and theoretical in-tensities qDS(q). Figure 10 b shows the corresponding experi-mental and theoretical difference radial intensity rDS(r). Duringglobal-fitting analysis, we used two-body dissociation (HgI2!HgI + I) as the primary dissociation pathway and optimized therate constants for two-body dissociation, geminate and nonge-minate recombination to HgI2, nongeminate formation of mo-lecular iodine, and included the laser beam size for the hydro-dynamics. The best fits are shown in Figure 10 a and b. Thefitted theoretical curves successfully reproduce experimentalcurves in both q and r space. The global-fitting analysis pro-

vides, as a function of time, population changes of all chemicalspecies (Figure 10 c) and temperature and density changes ofthe solvent (Figure 10 d). Figure 10 e summarizes the results.With 267 nm photoexcitation, (34�3.8) % of the excited HgI2

dissociates into HgI + I. Then (71�1.2) % of the transient HgIradical recombines nongeminately with atomic iodine that es-caped from other cages to re-form HgI2. On the other hand,(29�0.5) % of the iodine atoms recombine to form I2. The rateconstants for the nongeminate recombination of HgI2 and I2

were determined to be (5.0�0.5) � 1010 and (1.65�0.25) �1010

m�1 s�1, respectively.[66]

Before the thermal expansion starts, the solute dynamicsalone dominates over the cage (solute–solvent term) and sol-vent terms because of the heavy atoms (Hg and I) in thesolute. In Figure 11 a and b, the decomposition into solute,cage, and solvent contributions after 100 ps is shown. In theglobal fitting, the total difference signal is decomposed intothese contributions. As expected, the signal from the solutedominates over the entire q range; however, the contributionsfrom the cage and the solvent are not negligible at low q (Fig-ure 11 a). In Figure 11 b, the negative peak around 2.6 � ismainly due to the depletion of the Hg�I bond in HgI2 and for-mation of a new Hg�I bond in transient HgI.

Figure 9. Global-fitting analysis of TRXL data. After radial integration of thediffraction images, the difference curves are obtained after suitable scalingat high scattering angles. Theoretical curves for the solute-related terms arecalculated using the gi,j(r) functions from MD with putative solute structuresfrom quantum chemical calculations. In the global-fitting analysis, theoreticaldifference curves, at all time delays, are calculated for a given solute reactionincluding the hydrodynamic associated with that reaction (energy conserva-tion). Eventually the global fitting minimizes the difference between the the-oretical and experimental curves at all times simultaneously, and providesthe population of all the chemical species and the temperature, pressure,and density of the solvent environment as a function of time.

Figure 10. TXRL signals and fitting results for HgI2 in methanol. a) Experi-mental (black) and theoretical (red) difference intensities qDS(q) and theirerror bars in q space. The time delays from top to bottom are �100 ps,100 ps, 300 ps, 1 ns, 3 ns, 10 ns, 30 ns, 50 ns, 300 ns, and 1 ms. b) DifferenceRDFs, rDS(r). Shown are the sine-Fourier transforms of the intensities in (a).c) Concentration change of the photoreaction of HgI2 versus time. HgI, I, I2,and HgI2 are displayed in red, blue, green, and black lines, respectively.d) Change in the solvent density (red) and temperature (blue) as a functionof time. Note the duality between the decay in the excited-state populationin (c) and the rise in temperature in (d). e) Schematic reaction mechanism byTRXL for the photoreaction of HgI2. Pictures for the reaction mechanism aresnapshots from MD simulations.


H. Ihee et al.


The negative peak near 5.3 � corresponds to the I···I distancein the parent molecule. The positive peak at 3.5 � is assignedto a reorganization of the solvent around the truncated solute(new cage) and also to solvent heating, which leads to broad-ening of the methanol–methanol distance. These interpreta-tions can help in determining the primary reaction pathway inthe photodissociation of HgI2 in solution as follows. Four path-ways were considered: HgI2!HgI + I, HgI2!Hg + I + I, HgI2!Hg + I2, and the linear isomer reaction HgI2!HgI-I. The data atearly times (100 ps, 300 ps, and 1 ns) are fitted globally usingthe above primary reaction pathways. Figure 11 c and d showcomparisons of the fitted results for qDS(q) and rDS(r) forthese trial pathways. We can now rule out isomer formationbecause of the poor agreement between experiment andtheory. The fit for the two-body dissociation pathway matchesperfectly the experimental data over the entire q range andgives the smallest c2 value as compared to the other channels.The fits for the three-body dissociation and I2 formation chan-nels have a rather good figure of merit, but the fits are worse

than that for the two-body case. In fact, in the fits for thesechannels, the disagreements are significant for the positivepeak at 2 ��1 and the negative peak at 3 ��1. As shown in Fig-ure 11 a, the contribution from the solvent is not negligible.Thus, the apparent disagreements in this region for these twochannels clearly indicate that the solvent contribution fromthese channels is not consistent with the actual energy transferto the solvent. This tells us that when energetics is consideredin the analysis, the solvent contribution can help to discrimi-nate between candidate channels with very small differencesat high q. These results clearly demonstrate that TRXL deter-mines concurrently the structures of excited solutes in theircages and the structure and hydrodynamics of the solvent. It isalso shown that TRXL can be used as an ultrafast calorimeter,since the determination of transient structure (the primary dis-sociation channel) is strongly correlated with the energy trans-fer from solute and solvent molecules.

3.2. Elucidation of the Structure of Transient Species

Halogen elimination reactions from haloalkane are of particularinterest since the reaction products are under a stereochemicalcontrol related to the final positions of the functional groupswith respect to the newly formed C=C double bond.[67–70] Hal-oethyl radicals, such as CH2ICH2C and CF2ICF2C, form as inter-mediates of the halogen elimination reactions, and their struc-tures have been hypothesized to account for the observedstereoselectivity. In a symmetrically bridged structure, the halo-gen is shared equally between the two carbon atoms, whereasin a classical mixed structure (a mixture of anti and gaucheconformers) the primary halide resides predominantly on onecarbon atom.[70] A bridged structure of the intermediate pre-vents rotation about the C�C bond, thereby maintaining thefunctional group positions in the final product and providingstereochemical control. However, despite numerous theoreticaland experimental investigations on these reactions, the struc-ture of the intermediate in solution remained unknown. To un-ravel the structure of the intermediate and the related kineticsof this reaction, we applied TRXL to the iodine elimination re-actions of 1,2-diiodoethane (C2H4I2) and 1,2-tetrafluorodiiodo-ethane (C2F4I2) dissolved in methanol.[28, 33]

To explain the experimental data theoretically and fit the sig-nals globally, we included all putative structures in the global-fitting processes for both molecules. Our TRXL work hasshown that the iodine elimination reactions in C2H4I2 and C2F4I2

are completely different (Figure 12 c and e for C2H4I2 and Fig-ure 12 d and f for C2F4I2). The global-fitting results for iodineelimination in C2H4I2 show that C2H4I, I, and the C2H4I-I isomerare the dominant species after 100 ps and the formation ofC2H4 or I2 is not observed. C2H4I does not decay into C2H4 + I ;rather it reacts with an iodine atom to form an isomer, C2H4I-I,with a bimolecular rate constant of (7.94�3.48) �1011

m�1 s�1,[66] which is larger by two orders of magnitude than

the rate constant for nongeminate recombination of moleculariodine in CCl4 solvent.

This finding suggests that the isomer is mostly formed viain-cage recombination. The isomer, which is the major species

Figure 11. Contributions from the solute-only, solute–solvent (cage), and sol-vent–solvent correlations to the difference intensities and the differenceRDFs for HgI2 in methanol at 100 ps. The curve fitting is based on MD andexperimental solvent differentials and includes intramolecular and intermo-lecular contributions from the solutes and the solvent. The experimental(black, with experimental errors) and theoretical (red) qDS(q) (a) and corre-sponding rDS(r) (b) at 100 ps are shown. Also given are the decomposedcomponents: solute without cage (orange), cage effects (blue), and solventcontribution (green). Decomposed components of cage effects (blue) andthe solvent contribution (green) in (b) are multiplied by a factor of 3 to mag-nify major peaks and valleys. c) Determination of the photodissociationpathway of HgI2 in methanol at 100 ps. Theoretical (red) and experimental(black) difference intensities for candidate channels are shown as qDS(q)curves (c) and rDS(r) curves (d). The difference residuals between theoreticaland experimental curves are shown in blue. The two-body dissociation path-way (HgI2!HgI + I) gives the best fit.




in the nanoseconds regime, eventually decays into C2H4 + I2 inmicroseconds with a rate constant of (1.99�1.38) �105

m�1 s�1.[66] By contrast, C2F4I and I are major species at

100 ps as they are essentially formed within a few picosec-onds; (20�1.3) % of the C2F4I radicals decay to C2F4 + I with atime constant of (306�48) ps. We can compare these valueswith those for gas-phase electron diffraction: (55�5) % and(26�7) ps.[11, 15] This illustrates how solvent molecules greatlyreduce the rate and yield of secondary dissociation. That is notsurprising, as the available internal energy of the C2F4I radical

in solution is lower that in the gas phase due to the energytransfer to the solvent, which typically occurs in tens of pico-seconds. Molecular iodine I2 is formed concurrently by recom-bination of two iodine atoms in about 100 ns with a time con-stant of (4.4�1.25) � 1010

m�1 s�1,[66] which is comparable with

the rate constant for nongeminate recombination of moleculariodine in solution.

Of particular interest in these molecule systems is the struc-ture of the transient species. As mentioned, TRXL was the onlymethod that could answer the important question of whetherthe radical is bridged or classically open. We can calculate thediffraction patterns from putative intermediates and comparethose with the solvent-corrected experimental ones. The re-sults from this approach for C2H4I2 and C2F4I2 are shown in Fig-ure 12 a and b, respectively. The transient species alone arefound by subtracting the contributions from the solvent, cage,and other nascent solutes and are then compared with calcu-lated candidate molecules. This fingerprint approach is identi-cal to that used in gas-phase time-resolved electron diffraction.The comparison between the 100 ps data and the putative in-termediates demonstrates that the C2H4I radical has a bridgedstructure, whereas C2F4I is a mixture of a classical gauche andan anti conformer. In C2H4I, the negative peak at 5 �, the de-pletion of the I···I distance in the parent molecule, is commonfor both models. The peaks between 1 and 3 � are indeed de-pendent on the position of the I atom relative to the twocarbon atoms in the transient intermediate. Only the bridgedstructure matches the experimental peaks. Note that the antimodel has two peaks in this fingerprint region from the twodifferent C···I distances. For the C2F4I structure, the broad peakbetween 2 and 4 � is the fingerprint region. Only the classicalmixture structure of C2F4I reproduces the broad negative peakin the fingerprint region. The position and line shape of the3 � peak are very sensitive to the position of the iodine atomrelative to the two carbon atoms and the four fluorine atomsin the transient. Another argument for this structure assign-ment comes from the c2 values from the global fits for the twomodels. In the elimination reaction of C2F4I2, the c2 value forthe classical mixture is 1.7, which is smaller than the c2 valueof 3.2 for the bridged structure at all time delays. When bothmodels (bridged and classical mixture) are included in theglobal fits, the bridged fraction is almost zero. These findingsstrongly suggest that C2H4I is a bridged intermediate whereasC2F4I is a classical mixture, and support the fluorination effecton the radical that was predicted by quantum mechanical cal-culations.

3.3. Revealing Global and Major Reaction Pathways

In principle, diffraction probes the relative positions of allatom–atom pairs in the sample, which implies that no reactionpathway escapes detection to within the limits of the signal-to-noise ratio. In general, diffraction signals from all species aremixed in all diffraction angles whereas in the case of opticalspectroscopy, signals from different species can be well re-solved in the wavelength regime. Although diffraction offerslower sensitivity to those specific species and specific reaction

Figure 12. a) Structural determination of the 100 ps C2H4I radical in metha-nol. The C2H4I signal is obtained by subtracting other contributions from theraw data. This approach allows comparison of the solution structure withgas-phase structures of the anti and bridged conformers. Experimental(black) and theoretical (red) RDFs for the two channels are shown togetherwith their molecular structure (I : purple, C: gray and H: white). The upperand lower curves represent the bridged and classical anti structures, respec-tively. b) Structure determination of the 100 ps C2F4I radical in methanol. Thesolute-only term for the two candidate models (classical and bridged) areshown together with their molecular structure (I : purple, C: gray, and F:cyan). The data show that the C2H4I and C2F4I radicals have the bridged andclassical mixture structure, respectively. c,d) Reaction kinetics and populationchanges of the relevant chemical species during the photoelimination reac-tion for C2H4I2 (c) and C2F4I2 (d) in methanol as a function of time. In (c),black is bridged C2H4I, red is the isomer, and blue is the final product C2H4.In (d), green is the I atom, black is the classical form of C2F4I, red is C2F4, andblue is the I2 molecule. e) Reaction model of C2H4I2. After photoexcitation,one I atom is detached from the parent molecule, and the C2H4I radical isbridged. Then C2H4I recombines with another I atom to form a linear isomerC2H4I-I. Then the isomer breaks into C2H4 and I2. f) Reaction model of C2F4I2.After photoexcitation, one I atom is detached from the parent molecule, andC2F4I takes the classical anti form. Some C2F4I decays into C2F4 + I. TheI atoms finally recombine nongeminately into I2.


H. Ihee et al.


channels, the diffraction signals “integrate” all pathways and,in particular, the major channels. Therefore, TRXL provides aglobal picture of reaction kinetics with reliable branchingratios at the expense of sensitivity. The following examples, thephotodissociation dynamics of iodoform (CHI3) and carbon tet-rabromide (CBr4) in solution, stress this aspect of TRXL.[30, 32]

The photodissociation dynamics of dihaloalkane and triha-loalkane in solution have been extensively investigated by the-oretical and experimental methods. The main interest in thesesystems is the formation of a photoisomer upon UV excitationof low-lying electronic states. For example, iodoform dissoci-ates into CHI2 and I radicals upon excitation at 350 nm and iso-iodoform (CHI2-I) is reported to form via in-cage recombinationof the photofragments, with a time constant of 7 ps. Previousstudies with several time-resolved spectroscopic techni-ques,[71, 72] such as transient absorption and Raman spectrosco-py, suggest that isoiodoform is the major species with a quan-tum yield of ~0.5 in polar solvents (acetonitrile) and ~0.4 innonpolar solvents (cyclohexane) and with lifetimes of micro-seconds (acetonitrile) and hundreds of nanoseconds (cyclohex-ane). To probe the formation of isoiodoform and the followingdynamics, we applied TRXL to the photodissociation of iodo-form in methanol. Figure 13 a and b show the experimentalqDS(q) and rDS(r) curves and the corresponding theoreticalfits. To unravel the formation of isoiodoform, we tested twoseparate models: simple two-body dissociation (CHI3!CHI2 + I)and isomer formation (CHI3!CHI2-I). The c2 value for simpledissociation is nine times smaller than the isomer channel at10 ns, as shown in Figure 13 c and d. So isomer formation isnot in agreement with the experimental data at all. Moreover,when both models are included in the analysis, the contribu-tion from the isomer channel is negligible. DFT-optimizedstructures were used for all the putative species. The isomerhas three I···I distances (3.616, 3.304, and 6.181 �), and the C-I-Iangle is 1348. To check the possibility of isomers with other C-I-I angles, we varied the C-I-I angle from 134 to 908 in the anal-ysis. However, none of them fitted our experimental data. Thisresult indicates that isomer formation is not a major channelover the investigated time range from 100 ps to 3 ms, whichconflicts with the results from time-resolved optical spectro-scopy. Figure 13 e shows the reaction mechanism found byTRXL. Upon excitation at 266 nm, iodoform dissociates prompt-ly into CHI2 and I. Molecular iodine (I2) is formed by nongemi-nate recombination with a time constant of (1.55�0.25) �1010

m�1 s�1.[66] Other photoproducts, such as CHI3 and CHI2–

CHI2, formed by nongeminate recombination are not observed.The example demonstrates that TRXL offers an unbiasedmethod for capturing the major intermediate and its dynamics,which may not be resolved by optical spectroscopy. Althoughthe spectroscopic results indicated the existence of an isoiodo-form species with a subnanosecond lifetime, our TRXL data donot show any signal from this intermediate over the investigat-ed time range. The concentration of isoiodoform might be toolow to be detected by TRXL with the current signal-to-noiseratio. In addition, the formation of isoiodoform at times belowour 100 ps time resolution cannot be ruled out.

Carbon tetrahalides are important sources of reactive halo-gens that have been linked to ozone depletion in the tropo-sphere and stratosphere, and their photochemistry in the gasand solution phases has therefore become an active area ofexperimental interest.[73–75] Studies of the photodissociation ofCBr4 by time-resolved optical and X-ray absorption spectrosco-py have led to contradictory results. The time-resolved Ramanspectroscopic study showed that the Br2CBr-Br isomer isformed upon UV excitation with a lifetime of several nanosec-onds.[76] By contrast, time-resolved absorption spectroscopymeasurements indicated that excitation of CBr4 at 266 nm invarious polar and nonpolar solvents results in the formation ofa solvent-stabilized ion pair (CBr3

+//Br�)solvated with decay con-stants from subnanoseconds to microseconds dependent onthe solvent.[74] The time-resolved extended X-ray absorptionfine structure (EXAFS) study of CBr4 in cyclohexane did notshow any photodissociated reaction intermediate.[75] These dis-crepancies indicate that it would be useful to check CBr4 in sol-ution with the TRXL method because of its global sensitivity,as demonstrated with CHI3 above.

We have applied TRXL to CBr4 in methanol (Figure 14). Theglobal-fitting analysis showed the existence of new intermedi-

Figure 13. a) Global fits in reciprocal space. Experimental (black) and theo-retical (red) data for the photodissociation reaction of CHI3 in methanol.From top to bottom the time delay of each curve is �100 ps, 100 ps, 300 ps,1 ns, 3 ns, 6 ns, 10 ns, 30 ns, 45 ns, 60 ns, 300 ns, 600 ns, 1 ms, and 3 ms.b) Global fits in real space. c) Fitting result for the formation of CHI2 and I at10 ns. The molecular structure of CHI2 is also shown (I: purple and C: gray).d) Fitting result for the formation of CHI2�I isomer at 10 ns. The molecularstructure of the isomer is also shown (I: purple and C: gray). Black is experi-ment, red is theory, and green is residuals. The isomer fit is much worsethan that with simple two-body dissociation. When both channels are in-cluded in the fit, the isomer population converges to zero. e) Reactionmechanism for the photodissociation of iodoform as determined by TRXL.




ates that have not been observed in spectroscopic measure-ments. CBr3 and Br are the dominant species at early times (~100 ps), thus indicating that the C�Br bond is broken in CBr4

upon UV excitation. The Br radical rapidly decays into Br2 bynongeminate recombination with a rate constant of (0.65�2.3) � 1010

m�1 s�1.[66] Most of the CBr3 radicals decay back to

CBr4 through bimolecular recombination with Br. The main re-action of the CBr3 radical is escape from the solvation cageand teaming up with another CBr3 radical to produce C2Br6

with a rate constant of (0.55�1.3) � 109m�1 s�1,[66] which is an

order of magnitude slower than the recombination of two Bratoms into Br2. This finding can be rationalized by the relativesize of the Br and CBr3 radicals. The Br2CBr-Br isomer men-tioned previously, formed either by geminated recombinationin the cage or by the formation of an ion pair,[74, 76] cannot beobserved with the current signal-to-noise ratio, which indicatesthat these pathways are minor compared to those observedby TRXL. DFT calculation results show that the bimolecular re-combination of CBr3 is exothermic and C2Br6 can be producedwithout an energy barrier. However, the concentration of C2Br6

does not correlate with the decays of CBr3, which indicatesthat C2Br6 is not stable and dissociates quickly. According toour global fits, C2Br6 eventually decays to Br2 and a new spe-cies, C2Br4, as the final photoproducts in microseconds with arate constant of (2.9�3.3) � 106 s�1.[66] As the CHI3 and CBr4 ex-amples have shown, X-ray diffraction offers an important ad-

vantage: the scattered X-rays contain contributions from allchemical species within the sample simultaneously.

3.4. Unravelling New Intermediate Species

The TRXL method was applied to the solution-phase photo-chemistry of the transition-metal photocatalyst Ru3(CO)12 andthe binuclear complex [Pt2 ACHTUNGTRENNUNG(P2O5H2)4]4� (PtPOP). These mole-cules were selected as ideal targets due to their high scatteringpower and interesting photophysical and photochemical prop-erties.

The triangular metal carbonyl cluster Ru3(CO)12 is widelyused as a catalyst in controlled photoactivated synthesis inwhich specific bonds in the complex can be broken selectivelyat specific (excitation) wavelengths.[77, 78] The rearrangementand decomposition of Ru3(CO)12 are not only of fundamentalinterest but also of great practical importance. For this reasonthe photolysis of Ru3(CO)12 in solution has been extensively in-vestigated with various spectroscopic tools.[78–86] Ultrafast infra-red spectroscopic measurements show that photoexcitedRu3(CO)12 in a noncoordinating solvent such as cyclohexaneproduces two types of transient intermediates containingbridging carbonyl ligands: Ru3(CO)11ACHTUNGTRENNUNG(m-CO) (intermediate 1)from the metal–metal cleavage channel and Ru3(CO)10 ACHTUNGTRENNUNG(m-CO)for the CO loss reaction pathway (intermediate 2).[86] In thisstudy, the dynamics of these intermediates can only be unam-biguously identified by monitoring the distinct infrared absorp-tion from the bridging carbonyl groups. However, this leavesthe possibility of missing other intermediates, especially thosewith only terminal carbonyls where the absorption bands over-lap with those of the parent molecule (Figure 15 a). To addressthis issue, we applied TRXL to the dissociation of Ru3(CO)12 incyclohexane photoexcited at 390 nm in the low-energy band(Figure 15 b).[30]

Initial fits with intermediates 1 and 2 failed, which impliesthe existence of other intermediates. According to previousspectroscopic studies, the decay times of intermediates 1 and2 are 150 ps and 5 ns, respectively, and therefore the signal atlonger time delays should be dominated by the new inter-mediate. Thus, we fitted the experimental data at 30 ns withthe Debye scattering curves from putative structural transitions(Figure 15 c). The reaction pathway Ru3(CO)12!Ru3(CO)10 + 2 COmatches the experimental data well over the entire q range.The data analysis shows that the primary photoproduct is theRu3(CO)10 isomer. Only this isomer, with terminal carbonylgroups only (intermediate 3), reproduces the experimentalsignal whereas the other isomers, with bridging carbonyl li-gands, do not match the signal. This finding suggests that theultrafast infrared spectroscopic studies missed intermediate 3due to the absence of bridging carbonyl ligands.

To explain the time-resolved experimental data and to ex-tract the overall spatiotemporal kinetics, we performed global-fitting analysis by including the parent and intermediates 1–3.Figure 15 d shows the concentration changes of the relevantchemical species, as a function of time, determined by global-fitting analysis. After photoexcitation of Ru3(CO)12, intermedi-ate 1 [Ru3(CO)11ACHTUNGTRENNUNG(m-CO)] is formed from the metal–metal cleav-

Figure 14. a) Experimental data (black) and global fitting (red) in q spacefrom the photodissociation of CBr4 in methanol. From top to bottom, thetime delay of each curve is �100 ps, 100 ps, 300 ps, 500 ps, 700 ps, 1 ns,3 ns, 7 ns, 10 ns, 30 ns, 50 ns, 100 ns, 300 ns, 700 ns, 1 ms, and 5 ms. b) Experi-mental data (black) and the global fitting (red) in r space. c) Populationchange for each species as a function of time. Red is CBr3, olive is C2Br6, ma-genta is C2Br4, black is the Br atom, and blue is Br2. d) Schematic diagram ofthe photodissociation reaction pathways of CBr4 in methanol determined byTRXL.


H. Ihee et al.


age channel and decays exponentially to the initial Ru3(CO)12

with a unimolecular rate constant of (1.68�1.69) � 107 s�1.[66]

As this intermediate is a minor species (Figure 15 d), the erroris rather large unfortunately. Ac-tually a reasonable fit can be si-mulated without intermediate 1.On the contrary, intermediate 2[Ru3(CO)11ACHTUNGTRENNUNG(m-CO)] , which isformed from the CO-loss chan-nel, is necessary to generate areasonable fit. This intermediaterecombines nongeminately withCO to give the parent moleculewith a bimolecular rate constantof (3.27�0.19) � 1010

m�1 s�1.[66]

The major species, intermedi-ate 3 [Ru3(CO)10] , decays into in-termediate 2 by nongeminate re-combination with CO with a rateconstant of (1.88�0.08) �109

m�1 s�1.[66] As the decay of in-

termediate 3 is much slowerthan that of intermediate 2, any

intermediate with the formula Ru3(CO)11 is a candidate for theactual intermediate formed from nongeminate recombinationof intermediate 3 and CO. Therefore, the structure of the inter-mediate that connects intermediate 3 and the parent moleculecannot be determined. Since the Ru–Ru distances contributemore than 90 % to the coherent diffraction signal, an attemptwas made to optimize all the Ru–Ru distances in the parentmolecule and in the transient intermediates, by using a singlescale factor for the calculated Ru–Ru distances. The optimizedexperimental bond lengths are shorter than those from DFT,consistent with the general trend of DFT calculations to overes-timate the metal–metal distance. The Ru3(CO)12 case demon-strates that TRXL and ultrafast optical spectroscopy are com-plementary with each other. Intermediate 3 is invisible in infra-red spectroscopy, but has to be included in the TRXL data. Onthe other hand, TRXL alone cannot determine the existence ofa minor species such as intermediate 1, since its contributionto the overall diffraction is so weak compared to that of inter-mediate 3. Therefore, the results from the two complementarytechniques indicate the existence of at least three intermedi-ates with very different molecular structures and time con-stants.

TRXL has also been used to study the excited-state structureof the organometallic compound PtPOP. PtPOP has D4h symme-try with a square-planar configuration around two platinumatoms (Figure 16 a). As in other binuclear d8 complexes, thelowest electronic excitation is s*!s which results in a largecontraction along the metal–metal coordinate. The lowest ex-cited state of PtPOP has 3A2u symmetry. The lifetime of thelowest excited state is determined to be 9.8 ms in deoxygenat-ed water.[87] The quantum yield of 100 % for triplet formationin the upper states is also derived from photophysical data.[88]

Several methods have been applied to characterize the struc-tural parameters of the lowest excited state. Time-resolved X-ray absorption fine structure (XAFS) measurements derive(0.52�0.13) � inward movements of the P–P planes upon exci-tation into the 3A2u state in water.[89] An excited-state crystal

Figure 15. a) Molecular structure and intermediates in the photoreaction ofRu3(CO)12. Intermediate 1 is the result of Ru�Ru bond breaking, intermedi-ate 2 is the result of CO dissociation, and intermediate 3 is from dissociationof two CO groups. b) Comparison of experimental data (black) and theoreti-cal data (red) in q space. The time delays from top to bottom are �100 ps,42 ps, 60 ps, 75 ps, 100 ps, 200 ps, 300 ps, 500 ps, 1 ns, 3 ns, 5 ns, 10 ns,30 ns, 50 ns, 100 ns, and 300 ns. The values in the low-q region of the first13 curves and the last three curves have been divided by 3 and 6, respec-tively, for clarity. c) Determination of the photoproducts at 30 ns and charac-terization of intermediate 3. Experimental (black) and theoretical (red) differ-ence scattering intensities qDS(q) for various candidate reactions (top: inter-mediate 1, middle: intermediate 2, and bottom: intermediate 3) are shown.Intermediate 3 gives the best agreement between experiment and theory.d) Concentration change of the photoreaction of Ru3(CO)12 (black: intermedi-ate 1, blue: intermediate 2, red: intermediate 3, and cyan: Ru3(CO)12). Withinthe time resolution of 100 ps, three intermediates are observed and theyreturn to the parent molecule.

Figure 16. a) Model structures of the PtPOP anion, [Pt2ACHTUNGTRENNUNG(P2O5H2)4]4�, in the ground (1A1g) and lowest excited (3A2u)states without hydrogen atoms. The bond distances in both states are displayed. An 8 % contraction of Pt–Pt dis-tance occurs upon optical excitation (Pt: green, P: yellow, and O: red). b) Solute-only contributions at 100 ps (bluecircles) and 1 ms (red circles) and the fit (black line) from global maximum-likelihood analysis. In the experimentaland theoretical data, the bulk-solvent contribution is subtracted to emphasize the contribution to the differencediffraction signal from changes in the molecular structure of the solute. The decrease in the oscillation amplitudecorresponds to a lower population of the excited-state PtPOP at 1 ms.




structure at low temperatures has also been determined bytime-resolved X-ray diffraction. The Pt–Pt distance of the 3A2u

state was measured in a single crystal of (Et4N)3HPtPOP at cryo-genic temperatures with microsecond time resolution, and acontraction of 0.28 � was obtained.[90] Figure 16 b shows thesolute-only terms of the transient species (3A2u state) at 100 psand 1 ms. Information about key structural parameters is ob-tained by fitting a simulated difference signal [DSACHTUNGTRENNUNG(q,t)] for arange of hypothetical structures to the experimental data andevaluating the quality of the fit. In the present case, the keyparameters are the Pt–Pt distance and the distance betweenthe P planes. The analysis shows that the Pt–Pt distance in the3A2u state is (2.74�0.06) �, a contraction of 0.24 � or 8 % fromthe ground-state distance (2.98 �) from static X-ray diffraction.The contraction due to the optical excitation is in good agree-ment with earlier values from time-resolved resonance Ramanspectroscopy and diffraction data in the crystalline phase andfrom time-resolved EXAFS measurement in solution.[91] The dis-tance between the P planes in the 3A2u state is determined tobe (2.74�0.06) �, which is identical to the ground state withinexperimental accuracy. This finding implies a slight lengthen-ing of the Pt�P bond following excitation.

3.5. Thermal and Structural Dynamics of PhotoexcitedNanoparticles

Metal and semiconductor nanoparticles have been extensivelyinvestigated due to their nonlinear properties.[92, 93] A largenumber of ultrafast optical studies have focused on the transi-ent optical properties as a function of material, particle size,and embedding environment.[92] For example, time-resolvedoptical pump–probe measurements have shown that theenergy absorbed by electrons in metals after ultrafast excita-tion is transferred to the lattice via phonon emission within afew picoseconds, which leads to a homogeneous temperaturedistribution in each nanoparticle,[94, 95] and the nanoparticlescool down in less than a nanosecond.[95] However, it is difficultto address the structural properties by optical spectroscopicmethods, especially where nonreversible processes are con-cerned. Since X-ray scattering is sensitive to all structural relax-ations in the sample, TRXL makes it possible to track the struc-tural relaxations in the nanoparticles (heating, melting, and ex-plosion) and in the surround medium (explosive boiling).

Recently, the TRXL method has been applied to gold nano-particles suspended in water to obtain a time-resolved pictureof the structural and thermal dynamics of the nanoparticlesand adjacent medium following excitation with femtosecondlaser pulses.[96–100] The signals from the water solvent (wide-angle X-ray scattering, WAXS), the particle lattice (powder scat-tering), and the shape scattering from nanoparticles (small-angle X-ray scattering, SAXS) were used to determine thestructure of the particles as well as that of the local environ-ment (water). By detecting powder scattering from gold nano-particles as a function of time delay and laser fluence, the tran-sient heating and subsequent matrix cooling dynamics weremeasured. It was also found that the thermal relaxation can bemodeled quantitatively for a range of particle sizes between

10 and 100 nm.[96] At low excitation fluences, the measure-ments show regular cooling dynamics with a heat flow fromthe nanoparticles to the water medium. The thermal conduc-tivity in bulk water and in the particle/water interface affectsthe cooling process, which lasts for about a nanosecond forlarger particles.[95] By increasing the fluence, the water aroundthe nanoparticles reaches a critical temperature, which leads toexplosive evaporation (vapor-bubble formation).[98–99] Thesebubbles inhibit the cooling process on the subnanosecondtimescale. The nanoscale structure for this process has been re-solved directly by TRXL.[99] The nanoparticles themselves under-go a melting transition and fragment. The fragments form newparticles with sizes around 9 � on the microsecond time-scale.[100] It has been discovered that nonreversible mass re-moval from gold particles in water can be initiated below themelting point of the particles. By combining different scatter-ing methods in the pump–probe setup (small-angle scatteringand powder diffraction), it was shown that the (anisotropic)change in shape of nanoparticles occurs on the picosecondtimescale.

3.6. Protein Structural Dynamics

One can envision studying more complex molecules such asproteins by using TRXL. In the case of proteins in physiologicalmedia, the relatively low concentration (a few mm or less)makes TRXL measurements extremely difficult and the largemolecular size (more than a thousand times larger than smallmolecules) complicates the structural analysis. However, recentTRXL data from model proteins in solution have demonstratedthat the medium- to large-scale dynamics of proteins is rich ininformation on timescales from nanoseconds to millisec-onds.[101] Due to the inverse relationship between the intera-tomic distance and the scattering angle, the scattering frommacromolecules appears at smaller scattering angles in theSAXS/WAXS range. For this reason, the TRXL method appliedto protein samples is termed TR-SAXS/WAXS. The TR-SAXS/WAXS methodology has been applied to human hemoglobin(Hb), a tetrameric protein made of two identical a,b dimersthat is known to have at least two different quaternary struc-tures (a ligated stable “relaxed” (R) state and an unligatedstable “tense” (T) structure) in solution. The tertiary and quater-nary conformational changes of Hb triggered by laser-inducedligand dissociation have been identified with this method. Apreliminary analysis by the allosteric kinetic model gives atimescale for the R–T transition of ~1–3 ms, which is shorterthan the timescale derived with time-resolved optical spectro-scopy. In Figure 17 a, gas-phase scattering from the crystalstructures of HbCO and Hb (deoxyHb) are shown togetherwith one myoglobin (Mb) unit and a water molecule. In Figur-e 17 b, the relative change from the transition HbCO!Hb isshown for a 1 mm concentration. Note the good signal-to-background ratio between 0.1 and 1 ��1 due to weak scatter-ing on the low-q water “plateau”. Finally, the structures of theproteins and water are shown in Figure 17 c. The optically in-duced tertiary relaxation of Mb and the refolding of cytochro-me c have also been studied with TR-SAXS/WAXS.[101] The ad-


H. Ihee et al.


vantage of TR-SAXS/WAXS over time-resolved X-ray proteincrystallography is that it can probe irreversible reactions, as il-lustrated by the folding of cytochrome c, as well as reversiblereactions, such as ligand reactions in heme proteins. Althoughthe diffraction patterns from proteins in solution contain struc-tural information, the information content is probably insuffi-

cient to reconstruct proteinstructures on atomic scales. Inthis respect, the use of struc-tures from X-ray crystallographyand NMR spectroscopy as astarting point for refinementsagainst TR-SAXS/WAXS data ispromising and the developmentof an accurate theoretical analy-sis is in progress. The rate con-stants and lifetimes of all photo-reactions investigated by TRXLare assembled in Table 1.

4. Comparisons withOther Time-ResolvedTechniques

4.1. Comparison with Time-Resolved Optical Spectroscopy

To track time-dependent proc-esses, various time-resolvedspectroscopic tools have beendeveloped and reaction dynam-ics with femtosecond time reso-lution can now be routinely in-vestigated by such methods.Time-resolved optical spectro-scopy has been applied to

studying ultrafast events in various areas of chemistry, physics,and biology. A laser pulse triggers a photochemical reaction ora perturbation in the system and another laser pulse (withwavelength ranging from the ultraviolet to infrared or far infra-red) probes the optical responses of the system as a functionof time delay between pump and probe pulses as well as the

wavelength of the probe pulse.This method permits the detec-tion of specific short-lived spe-cies or energy states with veryhigh sensitivity. Unfortunately,the optical probe is not able tointerfere with all atoms and thusexperimental observables in op-tical spectroscopy, such as tran-sition energy and transition in-tensity, cannot provide directstructural information, such asatomic coordinates or at leastbond lengths and bond angles.In contrast, since the X-ray scat-tering probes all atom–atompairs in the molecular system,TRXL has unique capabilities todirectly access the structural dy-namics in the sample. In spite ofthe diffraction signal in TRXL

Figure 17. a) Calculated Debye scattering for hemoglobin (HbCO and Hb), myoglobin (Mb), and water. b) Relativechange of the protein signal to the water background for the R-to-T transition (HbCO!Hb) for an excited-stateconcentration of 1 mm. c) Snapshots of molecular structures used in the calculations of the scattering patterns.

Table 1. Rate constants for molecular systems studied by TRXL.

Solute/Solvent Reaction Values

C2H4I2/CH3OH C2H4I + I!C2H4I-I[a] 7.94ACHTUNGTRENNUNG(�3.48) � 1011

C2H4I-I!C2H4 + I2[b] 1.99ACHTUNGTRENNUNG(�1.38) � 105

HgI2/CH3OH HgI + I!HgI2[a] 5.0 ACHTUNGTRENNUNG(�0.5) � 1011

I + I!I2[a] 1.65ACHTUNGTRENNUNG(�0.3) � 1010

CHI3/CH3OH I + I!I2[a] 1.55ACHTUNGTRENNUNG(�0.3) � 1010

C2F4I2/CH3OH C2F4I!C2F4 + I[b] 3.27ACHTUNGTRENNUNG(�0.52) � 109

I + I!I2[a] 4.4 ACHTUNGTRENNUNG(�1.25) � 1010

CBr4/CH3OH CBr3 + CBr3!C2Br6[a] 0.55ACHTUNGTRENNUNG(�1.3) � 109

C2Br6!C2Br4 + Br2[b] 2.9 ACHTUNGTRENNUNG(�3.3) � 106

Br + Br!Br2[a] 0.65ACHTUNGTRENNUNG(�2.3) � 1010

Ru3(CO)12/C6H12 intermediate 1!parent[b] 1.68ACHTUNGTRENNUNG(�1.69) � 107

intermediate 2 + CO!parent[a] 3.27ACHTUNGTRENNUNG(�0.19) � 1010

intermediate 3 + CO!intermediate 2[a] 1.88ACHTUNGTRENNUNG(�0.08) � 109

[a] The values give the reaction constant in m�1 s�1. [b] The values give the reaction constant in s�1.




being less sensitive to a specific transient than optical spectro-scopy, its signal allows the direct observation of major transi-ent species and provides a global picture of the reactions withaccurate branching ratios between multiple reaction pathways,as shown in the examples in the previous sections. Since X-rays scatter from all atoms in the solution, solutes as well assolvent molecules, the analysis of TRXL data can provide thetemporal behavior of the solvent as well as the structural pro-gression of the solute molecules in all their reaction pathways,thus providing information on the rearrangement of the sol-vent around the transient solutes.

Vibrational transitions in a molecule can often be correlatedto specific vibrational motions of a molecule with characteristicvibrational frequencies and can be used to probe specific siteswithin molecular systems. For this reason time-resolved vibra-tional (IR and Raman) spectroscopies[102, 103] have been used forprobing transient structures in chemical reactions. However,the vibrational signals bias species with high absorption crosssection and these techniques may fail to detect optically silentspecies. In addition, it is often difficult to obtain insight intothe global structure from vibrational spectroscopy, and newapproaches, such as multidimensional IR and Raman spectros-copies, have emerged which are very promising in this re-spect.[104, 105] Two-dimensional spectroscopy measures the vibra-tion coupling between specific vibrational modes, which arecorrelated with the relative orientation of the molecule. The vi-bration–vibration coupling is very sensitive to molecular struc-ture by analogy to the spin–spin coupling in two-dimensionalNMR spectroscopy. Great progress has been made recently inresolving the molecular dynamics in biological systems by mul-tidimensional spectroscopy.

As shown in the examples in Section 3, time-resolved opticalspectroscopy and TRXL complement each other well. Theformer has a higher sensitivity and is thus useful for detectingextremely dilute reaction intermediates, whereas TRXL pro-vides direct structural information and accurate branchingratios.

4.2. Comparison with Time-Resolved X-ray AbsorptionSpectroscopy

X-ray absorption spectroscopy, such as X-ray absorption near-edge structure (XANES) and EXAFS, provide local structural in-formation and therefore the local response to laser excitationcan be obtained by these methods. The EXAFS region deliversquantitative structural information with sub-� accuracy via theso-called EXAFS equation,[48] whereas XANES provides a quanti-tative fingerprint of the local chemical bonding geometry, suchas orbital hybridization, in the vicinity of the atom(s) of inter-est. This can be useful for understanding molecular dynamicsin solution, where much important chemistry occurs, andwhere the solvent environment substantially influences reac-tion dynamics. Like TRXL, X-ray absorption spectroscopy hasalso been used in time-resolved studies with the laser pumpand X-ray probe scheme, and has been applied to studyingcharge-transfer[48–50, 106, 107] and spin-crossover processes[37, 108] incoordination chemistry compounds, solvation dynamics of

atomic radicals,[109] and structural dynamics of photodissociat-ed intermediates in the solution phase.[107, 110] The structural in-formation obtained by X-ray absorption is limited to the localenvironment of a particular atom. This feature is in contrast tothe diffraction method, which provides structural informationfor all species. The locality of the X-ray absorption signal hasthe advantage of a much higher sensitivity. In summary, TRXLand time-resolved X-ray absorption spectroscopy are highlycomplementary and thus, in the future, a combination of thetwo techniques may prove to be useful in providing more ac-curate results. Such efforts are in progress within the upgradeprogram at the ESRF for 2012.

5. Summary and Outlook

In this review we have outlined the experimental and theoreti-cal backgrounds of TRXL and given recent examples from pho-tochemical research of the liquid phase. Although TRXL haslimitations, it provides direct structural and kinetic informationon the reaction dynamics of chemical reactions in liquids. TRXLaddresses detailed information about the structural changesand spatiotemporal kinetics of reaction intermediates in all re-action pathways, temporal rearrangements of solvents aroundsolutes, and the related solvent hydrodynamics. For example,TRXL can aid in the understanding of major reaction pathways,as shown for CHI3 and CBr4, the TRXL results for which are dif-ferent from those with time-resolved optical spectroscopy.TRXL can also identify new intermediates, as illustrated for thephotolysis of Ru3(CO)12, where TRXL complements the resultsfrom time-resolved spectroscopy. Moreover, TRXL is capable ofproviding direct structural information that is difficult to obtainfrom time-resolved optical spectroscopy, such as the molecularstructure of intermediates involved in iodine elimination reac-tions from C2H4I2 and C2F4I2. In addition, TRXL has been appliedto the investigation of the structural dynamics of more compli-cated systems, such as nanoparticles and proteins in solution.

Increasing qmax from the current ~8 ��1 to 12 ��1 by usingharder X-rays will not only provide more data, but will also in-crease the accuracy of the scaling of RDF curves by givingaccess to the atomic limit where molecules scatter as the sumof independent atoms without structure. Multilayer X-rayoptics to provide X-rays with shorter wavelength (0.50 �) isbeing installed at ESRF on beamline ID09B. Application of theTRXL method to molecules without heavy atoms is a challengeto be overcome. Such systems require that the signal-to-noiseratio of scattering data should be improved. For example, toextract a ten times weaker signal (in general, the scatteringsignal is proportional to Z2), the data acquisition time shouldbe increased 100 times. This is unrealistic in current experimen-tal setups, but could be feasible with future X-ray sources witha much higher flux (see below). Chemical substitution withheavy atoms may also provide a solution. The time resolutionof TRXL is currently limited by the temporal length of X-raypulses produced by synchrotron radiation facilities (100 ps).This time resolution might be improved with next-generationsources, such as X-ray free-electron lasers and energy-recoverylinacs, which promise to deliver subpicosecond X-ray pulses


H. Ihee et al.


with increased photon flux and nearly full coherence. As theproposed ultrafast X-ray facilities (e.g. , X-ray free-electronlasers) come online, the time resolution might reach 100 fsand below. It will be possible to image atomic motions alongthe potential energy surface in real time and to monitor bondbreaking/formation and isomerization processes in the solutionphase. However, as the X-ray pulses become as short as a fewhundreds of femtoseconds or less, assumptions of thermallyequilibrated solute structure and hydrodynamic equations forsolvent responses will be no longer valid, which could compli-cate the theoretical analysis of TRXL data and structure deter-mination. As these challenges are overcome, TRXL will havegreat impact on the study of reaction dynamics.

Acknowledgements

We thank co-workers listed in many of the references of thisreview. This work was supported by the Creative Research Initia-tive (Center for Time-Resolved Diffraction) of MEST/KOSEF.

Keywords: liquids · photochemistry · structural dynamics ·time-resolved spectroscopy · X-ray diffraction

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